Related papers: Best Approximation Optimal Control for Infeasible …
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
We address long-standing open questions raised by Williamson, Goemans, Vazirani and Mihail pertaining to the design of approximation algorithms for problems in network design via the primal-dual method (Combinatorica 15(3):435-454, 1995).…
We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems,…
We develop a methodology for performing approximate optimal control simulations for quantum systems with multiple interacting degrees of freedom. The quantum dynamics are modeled using the first-order Magnus approximation in the interaction…
Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
We consider primal-dual pairs of semidefinite programs and assume that they are ill-posed, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…
In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…
Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…
The first nontrivial lower bound of the worst-case approximation ratio for the maxcut problem was achieved via the dual Cheeger problem, whose optimal value is referred to the dual Cheeger constant $h^+$, and later improved through its…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
In this work, we experimentally demonstrate an integrated circuit (IC) of 30 relaxation oscillators with reconfigurable capacitive coupling to solve the NP-Hard Maximum Cut (Max-Cut) problem. We show that under the influence of an external…
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…
In this contribution, we introduce an efficient method for solving the optimal control problem for an unconstrained nonlinear switched system with an arbitrary cost function. We assume that the sequence of the switching modes are given but…
The control and sensing of large-scale systems results in combinatorial problems not only for sensor and actuator placement but also for scheduling or observability/controllability. Such combinatorial constraints in system design and…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…